Numerical aperture

Describe a cone of light using its half-angle and the refractive index on the same side of the optical system.

Choose the side of the lens

For an axial point, NA = n sin u. Here u is the half-angle between the optical axis and the marginal ray, and n is the index of the medium at that point. Object-side and image-side numerical apertures can differ.

Keep the cone angle fixed

For u = 30° in air, NA = 1.00 × 0.5 = 0.50. For a 30° cone in water of index 1.33, NA = 0.665. These are two specified cones; an actual objective must be designed for its immersion medium.

Relate NA to f-number

For a thin lens in air focused at infinity, the paraxial approximation gives image-side NA ≈ 1/(2N). At large aperture or finite conjugates, use the actual marginal ray angle in image space.